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Card Trick 2

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Happy Numbers

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

Inequalities

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A bag contains 12 marbles. There are more red than green but taking the green and blue together exceeds the number of reds. The total number of yellow and green marbles is more than the total number of red and blue. Find exactly how many of each colour there are in the bag. How many different solutions can you find?